| Directions: In each of the following questions two equations are given. Solve these equations and give answer. [IBPS (SO) 2013] |
| I. \[10{{x}^{2}}-7x+1=0\] |
| II. \[35{{y}^{2}}-12y+1=0\] |
A) If \[x<y\]
B) If \[x>y\]
C) If \[x=y\]
D) If \[x\ge y\]
E) If \[x\le y\]
Correct Answer: D
Solution :
| I. \[10{{x}^{2}}-7x+1=0\] |
| \[\Rightarrow \]\[10{{x}^{2}}-5x-2x+1=0\] |
| \[\Rightarrow \]\[5x\,\,(2x-1)-1\,\,(2x-1)=0\] |
| \[\Rightarrow \]\[(5x-1)(2x-1)=0\] |
| \[\therefore \]\[x=\frac{1}{5},\]\[\frac{1}{2}\] |
| II. \[35{{y}^{2}}-12y+1=0\] |
| \[\Rightarrow \]\[35{{y}^{2}}-7y-5y+1=0\] |
| \[\Rightarrow \]\[7y\,\,(5y-1)-1\,\,(5y-1)=0\] |
| \[\Rightarrow \]\[(5y-1)(7y-1)=0\] |
| \[\therefore \]\[y=\frac{1}{5},\]\[\frac{1}{7}\] |
| Hence, \[x\ge y\] |
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